I think the setup doesn’t quite make sense for three reasons:
1 - The Born rule in Many worlds
I know this isn’t the main point of this post at all, but its important (I think) to remember that Bobs 99.99% “probability” argument doesn’t really make sense within any widely accepted version of many worlds.
Within Copenhagen (or Qubism, or most quantum interpretations) it is perfectly reasonable to posit a quantum state that responds to a measure with 99% chance of getting “heads”, eg. |psi> = sqrt(0.99) |1> + rest |0>.
However, many worlds claims that when this 99 to 1 state is measured in the computational basis the universe branches in 2 inone of which Bob sees the 1 and in the other he sees the 0. Experiment suggests that we see the |1> with 99% probability (this is the Born rule), which puts many worlds in a slightly odd place. There are (in my opinion rubbish) arguments that the universe splits in 2, but one branch is somehow more heavy (by factor 99) than the other. The (in my opinion) obvious suggestion that the universe splits into 100 branches, in 99 of which Bob sees a 1 and in one of which he sees a 0 is not widely popular, I think because people are worried about irrational numbers. Possibly they are also worried about what it actually means on a philosophical level to posit 99 different copies of a single world, all of which are completely impossible to distinguish from one another, even in principle. How is that actually different from 1 copy?
2 - Subjective Death
Lets say that we either find a way of incorporating the Born rule into many worlds that is fully convincing, or else we just sidestep the issue by using a very large number of 50⁄50 universe branches and kill Bob in all but one of them.
We now encounter what I see as a fundamental issue with the setup. Lets say that the quantum random number generator gives Bob a lethal dose of poison with 99.99% probability. He then experiences a 10 minute dying process from the poison. In the low-weight world branch where the machine doesn’t inject Bob does he have to wait 10 minutes for the versions of him in other worlds to die before he can believe in many worlds? If the machine had a tiny chance of giving him the poison then the poor, unlucky, envenomed Bob would not conclude that many worlds was true. So why the asymmetry in reasoning between dying and surviving?
This is a long-winded way of saying the post-selection to only worlds in which Bob survives is very suspect. Even if we accept that many worlds is true, then we end up in a state where their is one living Bob and 9999 dead (or dying) Bobs. I reject the supposition that the living Bob should update towards believing in many worlds. I also don’t believe that the dead (or dying) Bob’s should update against many worlds if they get the chance. If we assume that one day in the future technological resurrection [1] might be possible then suddenly those 9999 dead Bobs might get the chance to update against many worlds.
3 - Is “quantum” actually the source of the weirdness here
Leaving aside many worlds and its confusing-ness. Think about the conservation of expected evidence https://www.lesswrong.com/posts/jiBFC7DcCrZjGmZnJ/conservation-of-expected-evidence and how it is to be considered in cases where one (completely classical) possible outcome kills you immediately and prevents you from updating your beliefs. A man is playing Russian roulette with a classical pistol that kills him with 1/6 probability. He tells you that, if he shoots, he can always update towards knowing the bullet wasn’t in that chamber, because otherwise he wouldn’t be able to update at all. I am interested if you think that the quantum nature of the problem is actually introducing anything extra over this Russian roulette setup?
I think the setup doesn’t quite make sense for three reasons:
1 - The Born rule in Many worlds
I know this isn’t the main point of this post at all, but its important (I think) to remember that Bobs 99.99% “probability” argument doesn’t really make sense within any widely accepted version of many worlds.
Within Copenhagen (or Qubism, or most quantum interpretations) it is perfectly reasonable to posit a quantum state that responds to a measure with 99% chance of getting “heads”, eg. |psi> = sqrt(0.99) |1> + rest |0>.
However, many worlds claims that when this 99 to 1 state is measured in the computational basis the universe branches in 2 in one of which Bob sees the 1 and in the other he sees the 0. Experiment suggests that we see the |1> with 99% probability (this is the Born rule), which puts many worlds in a slightly odd place. There are (in my opinion rubbish) arguments that the universe splits in 2, but one branch is somehow more heavy (by factor 99) than the other. The (in my opinion) obvious suggestion that the universe splits into 100 branches, in 99 of which Bob sees a 1 and in one of which he sees a 0 is not widely popular, I think because people are worried about irrational numbers. Possibly they are also worried about what it actually means on a philosophical level to posit 99 different copies of a single world, all of which are completely impossible to distinguish from one another, even in principle. How is that actually different from 1 copy?
2 - Subjective Death
Lets say that we either find a way of incorporating the Born rule into many worlds that is fully convincing, or else we just sidestep the issue by using a very large number of 50⁄50 universe branches and kill Bob in all but one of them.
We now encounter what I see as a fundamental issue with the setup. Lets say that the quantum random number generator gives Bob a lethal dose of poison with 99.99% probability. He then experiences a 10 minute dying process from the poison. In the low-weight world branch where the machine doesn’t inject Bob does he have to wait 10 minutes for the versions of him in other worlds to die before he can believe in many worlds? If the machine had a tiny chance of giving him the poison then the poor, unlucky, envenomed Bob would not conclude that many worlds was true. So why the asymmetry in reasoning between dying and surviving?
This is a long-winded way of saying the post-selection to only worlds in which Bob survives is very suspect. Even if we accept that many worlds is true, then we end up in a state where their is one living Bob and 9999 dead (or dying) Bobs. I reject the supposition that the living Bob should update towards believing in many worlds. I also don’t believe that the dead (or dying) Bob’s should update against many worlds if they get the chance. If we assume that one day in the future technological resurrection [1] might be possible then suddenly those 9999 dead Bobs might get the chance to update against many worlds.
3 - Is “quantum” actually the source of the weirdness here
Leaving aside many worlds and its confusing-ness. Think about the conservation of expected evidence https://www.lesswrong.com/posts/jiBFC7DcCrZjGmZnJ/conservation-of-expected-evidence and how it is to be considered in cases where one (completely classical) possible outcome kills you immediately and prevents you from updating your beliefs. A man is playing Russian roulette with a classical pistol that kills him with 1/6 probability. He tells you that, if he shoots, he can always update towards knowing the bullet wasn’t in that chamber, because otherwise he wouldn’t be able to update at all. I am interested if you think that the quantum nature of the problem is actually introducing anything extra over this Russian roulette setup?
[1] or redaction! https://www.lesswrong.com/posts/CKgPFHoWFkviYz7CB/the-redaction-machine
I had a lot of fun with this idea. Made it into a little joke story: https://www.lesswrong.com/posts/zLYBzJttYy49LTpt6/quantum-immortality-foiled